Are you for one or the other? Or both?
My understanding is unit tests:
Unit Tests - my specific function does what it's supposed to do, nothing more, and nothing less.
Acceptance Test - my application does what it's supposed to do.
Example: Application to calculate roots of quadratic functions. Takes inputs of a, b, and c, returns roots x1 and x2. This application is built by functions I write to add two numbers, subtract two numbers, multiply two numbers, divide two numbers, and take the square root of two numbers.
Unit tests - check that my divide and multiply functions work correctly, my square root works correctly, my add and subtract work correctly.
Acceptance tests - check that my application calculates roots of quadratic functions.
Since my entire application is to calculate roots, I should not have a unit test that also calculates roots because there is no individual function which does so.